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Proof step 5 from proof path-nodups-subset (previous step)

r ∈ H, path(r ' + x0, H), # H ≤ # x0 ⊦ dups(x0), r ∈ x0, path(x0, H -- r)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ path(x, H) ∧ ¬ r ∈ x → path(x, H -- r)
Proof step 4:
¬ (path(x0, H) ∧ ¬ r ∈ x0), r ∈ H, path(r ' + x0, H), # H ≤ # x0 ⊦ dups(x0), r ∈ x0, path(x0, H -- r)

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: path-delnonmember antecedent: succedent: path(x, H) ∧ ¬ r ∈ x → path(x, H -- r) substlist: [r, H, x] → [r, H, x0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r, H, x0)]]